Journal of Combinatorial Designs最新文献
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Dual incidences and t-designs in vector spaces
向量空间中的对偶关联和t-设计
IF 0.7
4区 数学
Kristijan Tabak
{"title":"Dual incidences and t-designs in vector spaces","authors":"Kristijan Tabak","doi":"10.1002/jcd.21922","DOIUrl":"https://doi.org/10.1002/jcd.21922","url":null,"abstract":"<p>Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation> $V$</annotation>\u0000 </semantics></math> be an <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math>-dimensional vector space over <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <mi>q</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{F}}}_{q}$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal H} }}$</annotation>\u0000 </semantics></math> is any set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-dimensional subspaces of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation> $V$</annotation>\u0000 </semantics></math>. We construct two incidence structures <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>D</mi>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mi>a</mi>\u0000 \u0000 <mi>x</mi>\u0000 </mrow>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${{mathscr{D}}}_{max}({rm{ {mathcal H} }})$</annotation>\u0000 </semantics></math> and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>D</mi>\u0000 \u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mi>i</mi>\u0000 \u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>H</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> ${{mathscr{D}}}_{min}({rm{ {mathcal H} }})$</annotation>\u0000 </semantics></math> using subspaces from <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> ${rm{ {mathcal H} }}$</annotation>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 1","pages":"46-52"},"PeriodicalIF":0.7,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134805714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Completing the solution of the directed Oberwolfach problem with cycles of equal length
完成了等长环有向Oberwolfach问题的求解
IF 0.7
4区 数学
Alice Lacaze-Masmonteil
{"title":"Completing the solution of the directed Oberwolfach problem with cycles of equal length","authors":"Alice Lacaze-Masmonteil","doi":"10.1002/jcd.21918","DOIUrl":"https://doi.org/10.1002/jcd.21918","url":null,"abstract":"<p>In this paper, we give a solution to the last outstanding case of the directed Oberwolfach problem with tables of uniform length. Namely, we address the two-table case with tables of equal odd length. We prove that the complete symmetric digraph on <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $2m$</annotation>\u0000 </semantics></math> vertices, denoted <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>K</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <mo>*</mo>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation> ${K}_{2m}^{* }$</annotation>\u0000 </semantics></math>, admits a resolvable decomposition into directed cycles of odd length <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $m$</annotation>\u0000 </semantics></math>. This completely settles the directed Oberwolfach problem with tables of uniform length.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 1","pages":"5-30"},"PeriodicalIF":0.7,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21918","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134880386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Orthogonal cycle systems with cycle length less than 10
周期长度小于10的正交循环系
IF 0.7
4区 数学
Selda Küçükçifçi, Emine Şule Yazıcı
{"title":"Orthogonal cycle systems with cycle length less than 10","authors":"Selda Küçükçifçi, Emine Şule Yazıcı","doi":"10.1002/jcd.21921","DOIUrl":"https://doi.org/10.1002/jcd.21921","url":null,"abstract":"<p>An <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decomposition of a graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is a partition of the edge set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> into subsets, where each subset induces a copy of the graph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>. A <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-orthogonal <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decomposition of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> is a set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decompositions of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> such that any two copies of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math> in distinct <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decompositions intersect in at most one edge. When <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mo>=</mo>\u0000 <msub>\u0000 <mi>K</mi>\u0000 <mi>v</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> $G={K}_{v}$</annotation>\u0000 </semantics></math>, we call the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <annotation> $H$</annotation>\u0000 </semantics></math>-decompositi","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"32 1","pages":"31-45"},"PeriodicalIF":0.7,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134814340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalizations of some Nordhaus–Gaddum-type results on spectral radius
谱半径上某些Nordhaus–Gaddum型结果的推广
IF 0.7
4区 数学
Junying Lu, Lanchao Wang, Yaojun Chen
{"title":"Generalizations of some Nordhaus–Gaddum-type results on spectral radius","authors":"Junying Lu, Lanchao Wang, Yaojun Chen","doi":"10.1002/jcd.21919","DOIUrl":"https://doi.org/10.1002/jcd.21919","url":null,"abstract":"<p>Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> be a simple graph and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>G</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $lambda (G)$</annotation>\u0000 </semantics></math> the spectral radius of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. For <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation> $kge 2$</annotation>\u0000 </semantics></math>, a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-edge decomposition <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <msub>\u0000 <mi>H</mi>\u0000 \u0000 <mn>1</mn>\u0000 </msub>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>…</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <msub>\u0000 <mi>H</mi>\u0000 \u0000 <mi>k</mi>\u0000 </msub>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation> $({H}_{1},{rm{ldots }},{H}_{k})$</annotation>\u0000 </semantics></math> is <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math> spanning subgraphs such that their edge sets form a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 </mrow>\u0000 <annotation> $k$</annotation>\u0000 </semantics></math>-partition of the edge set of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math>. In this paper, we obtain some sharp lower and upper bounds for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 12","pages":"701-712"},"PeriodicalIF":0.7,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50153173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Construction of rank 4 self-dual association schemes inducing three partial geometric designs
诱导三个局部几何设计的秩为4的自对偶关联方案的构造
IF 0.7
4区 数学
Akihide Hanaki
{"title":"Construction of rank 4 self-dual association schemes inducing three partial geometric designs","authors":"Akihide Hanaki","doi":"10.1002/jcd.21917","DOIUrl":"https://doi.org/10.1002/jcd.21917","url":null,"abstract":"<p>Xu characterized rank 4 self-dual association schemes inducing three partial geometric designs by their character tables. We construct such association schemes as Schur rings over Abelian 2-groups.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 12","pages":"691-700"},"PeriodicalIF":0.7,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50122308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
proper partial geometries with an automorphism group acting primitively on points and lines
自同构群初始作用于点和线的适当局部几何
IF 0.7
4区 数学
Wendi Di
{"title":"proper partial geometries with an automorphism group acting primitively on points and lines","authors":"Wendi Di","doi":"10.1002/jcd.21914","DOIUrl":"https://doi.org/10.1002/jcd.21914","url":null,"abstract":"<p>Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{S}}$</annotation>\u0000 </semantics></math> be a finite proper partial geometry pg<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>s</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>t</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>α</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $(s,t,alpha )$</annotation>\u0000 </semantics></math> not isomorphic to the van Lint–Schrijver partial geometry pg<math>\u0000 <semantics>\u0000 <mrow>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mn>5</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>5</mn>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $(5,5,2)$</annotation>\u0000 </semantics></math> and let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> be a group of automorphisms of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{S}}$</annotation>\u0000 </semantics></math> acting primitively on both points and lines of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>S</mi>\u0000 </mrow>\u0000 <annotation> ${mathscr{S}}$</annotation>\u0000 </semantics></math>, we show that if <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>α</mi>\u0000 \u0000 <mo>≤</mo>\u0000 \u0000 <mn>60</mn>\u0000 </mrow>\u0000 <annotation> $alpha le 60$</annotation>\u0000 </semantics></math> then <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $G$</annotation>\u0000 </semantics></math> must be almost simple.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 11","pages":"642-664"},"PeriodicalIF":0.7,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50148812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
P℘N functions, complete mappings and quasigroup difference sets
P℘N函数、完备映射与拟群差集
IF 0.7
4区 数学
Nurdagül Anbar, Tekgül Kalaycı, Wilfried Meidl, Constanza Riera, Pantelimon Stănică
{"title":"P℘N functions, complete mappings and quasigroup difference sets","authors":"Nurdagül Anbar, Tekgül Kalaycı, Wilfried Meidl, Constanza Riera, Pantelimon Stănică","doi":"10.1002/jcd.21916","DOIUrl":"https://doi.org/10.1002/jcd.21916","url":null,"abstract":"<p>We investigate pairs of permutations <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>G</mi>\u0000 </mrow>\u0000 <annotation> $F,G$</annotation>\u0000 </semantics></math> of <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <msup>\u0000 <mi>p</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{F}}}_{{p}^{n}}$</annotation>\u0000 </semantics></math> such that <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 \u0000 <mo>+</mo>\u0000 \u0000 <mi>a</mi>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>x</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $F(x+a)-G(x)$</annotation>\u0000 </semantics></math> is a permutation for every <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>a</mi>\u0000 \u0000 <mo>∈</mo>\u0000 \u0000 <msub>\u0000 <mi>F</mi>\u0000 \u0000 <msup>\u0000 <mi>p</mi>\u0000 \u0000 <mi>n</mi>\u0000 </msup>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> $ain {{mathbb{F}}}_{{p}^{n}}$</annotation>\u0000 </semantics></math>. We show that, in that case, necessarily <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>x</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 \u0000 <mo>=</mo>\u0000 \u0000 <mi>℘</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mi>x</mi>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 ","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 12","pages":"667-690"},"PeriodicalIF":0.7,"publicationDate":"2023-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50141470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the directed Oberwolfach problem for complete symmetric equipartite digraphs and uniform-length cycles
关于完全对称等分有向图和一致长环的有向Oberwolfach问题
IF 0.7
4区 数学
Nevena Francetić, Mateja Šajna
{"title":"On the directed Oberwolfach problem for complete symmetric equipartite digraphs and uniform-length cycles","authors":"Nevena Francetić, Mateja Šajna","doi":"10.1002/jcd.21913","DOIUrl":"https://doi.org/10.1002/jcd.21913","url":null,"abstract":"<p>We examine the necessary and sufficient conditions for a complete symmetric equipartite digraph <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>K</mi>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mrow>\u0000 <mo>[</mo>\u0000 \u0000 <mi>m</mi>\u0000 \u0000 <mo>]</mo>\u0000 </mrow>\u0000 </mrow>\u0000 \u0000 <mo>*</mo>\u0000 </msubsup>\u0000 </mrow>\u0000 <annotation> ${K}_{n[m]}^{* }$</annotation>\u0000 </semantics></math> with <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation> $n$</annotation>\u0000 </semantics></math> parts of size <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation> $m$</annotation>\u0000 </semantics></math> to admit a resolvable decomposition into directed cycles of length <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>. We show that the obvious necessary conditions are sufficient for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>n</mi>\u0000 \u0000 <mo>,</mo>\u0000 \u0000 <mi>t</mi>\u0000 \u0000 <mo>≥</mo>\u0000 \u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation> $m,n,tge 2$</annotation>\u0000 </semantics></math> in each of the following four cases: (i) <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 \u0000 <mrow>\u0000 <mo>(</mo>\u0000 \u0000 <mrow>\u0000 <mi>n</mi>\u0000 \u0000 <mo>−</mo>\u0000 \u0000 <mn>1</mn>\u0000 </mrow>\u0000 \u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $m(n-1)$</annotation>\u0000 </semantics></math> is even; (ii) <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mtext>gcd</mtext>\u0000 \u0000 <mrow>\u0000 <mo>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 11","pages":"604-641"},"PeriodicalIF":0.7,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jcd.21913","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50140497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A generalization of group divisible t $t$ -designs
群可整除t$t$-设计的一个推广
IF 0.7
4区 数学
Sijia Liu, Yue Han, Lijun Ma, Lidong Wang, Zihong Tian
{"title":"A generalization of group divisible \u0000 \u0000 \u0000 t\u0000 \u0000 $t$\u0000 -designs","authors":"Sijia Liu, Yue Han, Lijun Ma, Lidong Wang, Zihong Tian","doi":"10.1002/jcd.21912","DOIUrl":"https://doi.org/10.1002/jcd.21912","url":null,"abstract":"<p>Cameron defined the concept of generalized <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-designs, which generalized <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-designs, resolvable designs and orthogonal arrays. This paper introduces a new class of combinatorial designs which simultaneously provide a generalization of both generalized <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-designs and group divisible <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-designs. In certain cases, we derive necessary conditions for the existence of generalized group divisible <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-designs, and then point out close connections with various well-known classes of designs, including mixed orthogonal arrays, factorizations of the complete multipartite graphs, large sets of group divisible designs, and group divisible designs with (orthogonal) resolvability. Moreover, we investigate constructions for generalized group divisible <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 <annotation> $t$</annotation>\u0000 </semantics></math>-designs and almost completely determine their existence for <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation> $t=2,3$</annotation>\u0000 </semantics></math> and small block sizes.</p>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 11","pages":"575-603"},"PeriodicalIF":0.7,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50137077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cameron–Liebler sets for maximal totally isotropic flats in classical affine spaces
经典仿射空间中最大全各向同性平面的Cameron–Liebler集
IF 0.7
4区 数学
Jun Guo, Lingyu Wan
{"title":"Cameron–Liebler sets for maximal totally isotropic flats in classical affine spaces","authors":"Jun Guo, Lingyu Wan","doi":"10.1002/jcd.21909","DOIUrl":"https://doi.org/10.1002/jcd.21909","url":null,"abstract":"<p>Let <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>C</mi>\u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>ν</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $ACG(2nu ,{{mathbb{F}}}_{q})$</annotation>\u0000 </semantics></math> be the <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>ν</mi>\u0000 </mrow>\u0000 <annotation> $2nu $</annotation>\u0000 </semantics></math>-dimensional classical affine space with parameter <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>e</mi>\u0000 </mrow>\u0000 <annotation> $e$</annotation>\u0000 </semantics></math> over a <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation> $q$</annotation>\u0000 </semantics></math>-element finite field <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathbb{F}}}_{q}$</annotation>\u0000 </semantics></math>, and <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mi>ν</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathscr{O}}}_{nu }$</annotation>\u0000 </semantics></math> be the set of all maximal totally isotropic flats in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 <mi>C</mi>\u0000 <mi>G</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>ν</mi>\u0000 <mo>,</mo>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>q</mi>\u0000 </msub>\u0000 </mrow>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation> $ACG(2nu ,{{mathbb{F}}}_{q})$</annotation>\u0000 </semantics></math>. In this paper, we discuss Cameron–Liebler sets in <math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>O</mi>\u0000 <mi>ν</mi>\u0000 </msub>\u0000 </mrow>\u0000 <annotation> ${{mathscr{O}}}_{nu }$</annotation>\u0000 </semantics></math>","PeriodicalId":15389,"journal":{"name":"Journal of Combinatorial Designs","volume":"31 11","pages":"547-574"},"PeriodicalIF":0.7,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50137650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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